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dc.contributor.authorShatashvili, Samsonen
dc.date.accessioned2022-05-16T13:18:32Z
dc.date.available2022-05-16T13:18:32Z
dc.date.issued2021en
dc.date.submitted2021en
dc.identifier.citationAlekseev, A. and Shatashvili, S.L., Characters, coadjoint orbits and Duistermaat-Heckman integrals, Journal of Geometry and Physics, 170, 104386, 2021en
dc.identifier.otherYen
dc.identifier.urihttp://hdl.handle.net/2262/98611
dc.description.abstractThe asymptotics of characters of irreducible representations of a compact Lie group G for large values of the scaling factor k are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of G. This phenomenon generalises to coadjoint orbits of central extensions of loop groups and of diffeomorphisms of the circle . We show that the asymptotics of characters of integrable modules of affine Kac-Moody algebras and of the Virasoro algebra factorize into a divergent contribution of the standard form and a convergent contribution which can be interpreted as a formal DH orbital integral. For some Virasoro modules, our results match formal DH integrals recently computed by Stanford and Witten. In this case, the k-scaling has the same origin as the one which gives rise to classical conformal blocks. Furthermore, we consider reduced spaces of Virasoro coadjoint orbits and we suggest a new invariant which replaces symplectic volume in the infinite dimensional situation. We also consider other modules of the Virasoro algebra (in particular, the modules corresponding to minimal models) and we obtain DH-type expressions which do not correspond to any Virasoro coadjoint orbits. We introduce volume functions corresponding to formal DH integrals over coadjoint orbits of the Virasoro algebra and show that they are related by the Hankel transform to spectral densities recently studied by Saad, Shenker and Stanford.en
dc.relation.ispartofseriesJournal of Geometry and Physicsen
dc.relation.ispartofseries170en
dc.relation.ispartofseries104386en
dc.rightsYen
dc.subjectcompact Lie group Gen
dc.subjectDuistermaat-Heckman (DH) integralsen
dc.subjectVirasoro algebraen
dc.subject.lcshcompact Lie group Gen
dc.subject.lcshDuistermaat-Heckman (DH) integralsen
dc.subject.lcshVirasoro algebraen
dc.titleCharacters, coadjoint orbits and Duistermaat-Heckman integralsen
dc.typeJournal Articleen
dc.type.supercollectionscholarly_publicationsen
dc.type.supercollectionrefereed_publicationsen
dc.identifier.peoplefinderurlhttp://people.tcd.ie/shatassen
dc.identifier.rssinternalid243162en
dc.identifier.doihttp://dx.doi.org/10.1016/j.geomphys.2021.104386en
dc.rights.ecaccessrightsopenAccess


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